Rachel Dolezal is a Caucasian woman (that is, a child of two Caucasian parents, as attested by a birth certificate and a physical resemblance). These days, she says, she "identifies as Black." She doesn't like the term "African American," possibly because it has more of a hard-edged, biological component to it. "Black," however, is more flexible. (Update: Bingo! In a recent interview, she says "I wouldn’t say I’m African American, but I would say I’m black, and there’s a difference in those terms."). "Black" can refer to a culture as much as it can to an ancestry, and to a socially imposed status as much as to either of its other meanings, so "Black" is what she calls herself.
She also identifies as the mother of one of her adopted brothers, of whom she has custody, and as the daughter of a black man named Albert Wilkerson. She also identifies as having been born in a teepee, having some Native American ancestry, having hunted for food with a bow and arrow in her childhood, and having lived in South Africa. None of these statements appears to be true.
Finally, she identifies as having been persecuted through her life. She says that, as a child, she and the other children were scourged by her parents with a whip that she likens to a slave whip. The blackest children in the family were, she says, whipped more severely. (Her brothers deny having been whipped). As an adult, she identifies as the victim of hate crimes that were duly reported to the police. No arrests have been made. In fact, circumstantial evidence points to her being the person responsible for at least some of these alleged hate crimes.
The number of false statements that she has made or let stand are either evidence of lying, if she knows they are false, or confabulation, if she doesn't.
As I've read the unfolding oddness of Dolezal's story, I've also read the passionate opinions of people who say that she has every right to call herself black and those of people (many of them black) who say she has no such right. I think the opinions depend on how the speakers conceive of their own identities.
Some people say that they are this or that--English, Chinese, Christian, male, old, socialist, or whatever; they fall into these categories quite unproblematically and without volition. As Dolezal describes the process, "I was socially conditioned … to be limited to whatever biological identity was being thrust upon me and being narrated to me." So, pretty much, is true of everyone. For many of us, the conditioning sticks.
However, others say that they identify as a member of this or that category. In many cases, there may be a genetic or hormonal reason for denying an assigned identity in favour of some other one. However, I don't think that most people who come out as, say, homosexual or transsexual necessarily "Deny thy father and refuse thy name" (as Juliet asks of Romeo). Dolezal did.
I think that a person who is his identity has a hard time understanding one who only identifies with it, and the opposite is just as true. Essentialists don't understand existentialists, and vice versa. So, we have much shouting over whether the white woman Rachel Dolezal can rightfully claim to be a black woman.
NOTE: The excellent site snopes.com now has a page on Rachel Dolezal which I assume will be kept up to date.